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Jun 28, 2010 at 10:58 comment added Bugs Bunny Agree, but it suffices to have an orientation on the normal bundle (on the curve to the surface).
Jun 25, 2010 at 11:10 vote accept Jun Lu
Jun 24, 2010 at 15:21 comment added Ben Wieland That's correct, but it turns out that the answer depends not on the orientation of the curve, but on the orientation of the surface. In particular, "the right side" doesn't make sense unless the surface is also oriented. And it turns out that the isotopy class of the diffeomorphism doesn't depend on the orientation of the curve. This is discussed in the primer Sam Nead linked to.
Jun 24, 2010 at 9:23 history edited Bugs Bunny CC BY-SA 2.5
added 36 characters in body
Jun 24, 2010 at 8:52 history answered Bugs Bunny CC BY-SA 2.5